Problem: What's the first wrong statement in the proof below that $ \triangle ABC \cong \triangle EBC$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle BED \cong \angle BAC$ $, \ $ $ \overline{DE} \cong \overline{AC}$ $, \ $ $ \angle BDE \cong \angle ACB$ $, \ $ $ \overline{CF} \cong \overline{BC}$ $, \ $ $ \angle CFE \cong \angle ABC$ $, \ $ and $\ $ $ \angle CEF \cong \angle BAC$ Proof $ \triangle ABC \cong \triangle EBD$ because ASA $ \overline{AB} \cong \overline{BE}$ because corresponding parts of congruent triangles are congruent $ \triangle EBC \cong \triangle EFC$ because SAS $ \triangle ABC \cong \triangle EFC$ because AAS $ \overline{BE} \cong \overline{EF}$ because corresponding parts of congruent triangles are congruent $ \triangle ABC \cong \triangle EBC$ because SSS
Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \triangle EFC \cong \triangle EBC$ is the first wrong statement.